Lista de exercícios do ensino médio para impressão
Resolver as seguintes equações:
a)
$\phantom{X}cos x = -\dfrac{ 1 }{ 2 }\phantom{X}$
b)
$\phantom{X}cos\,x\,=\,-\,\dfrac{\,\sqrt{\,2\,}\,}{\,2\,}\phantom{X}$
c)
$\phantom{X}cos\,x\,=\,\dfrac{\,\sqrt{\,3\,}\,}{\,2\,}\phantom{X}$
d)
$\phantom{X}sec\,x\,=\,\,2\phantom{X}$
e)
$\phantom{X}2\,\centerdot\,cos^2\,x\,=\,cos\,x\phantom{X}$
f)
$\phantom{X}4\,\centerdot\,cos\,x\,+\,3\,sec\,x\,=\,8\phantom{X}$
g)
$\phantom{X}2\,-\,2\,\centerdot\,cos\,x\,=\,sen\,x\,\centerdot\,tg\,x\phantom{X}$
h)
$\phantom{X}2\,\centerdot\,sen^2\,x\,+\,6\,\centerdot\,cos\,x\,=\,5\,+\,cos\,2x\phantom{X}$
i)
$\phantom{X}1\,+\,3\,\centerdot\,tg^2\,x\,=\,5\,\centerdot\,sec\,x\phantom{X}$
j)
$\phantom{X}\left(\,4\,-\,\dfrac{3}{sen^2x}\right)\,\centerdot\,\left(\,4\,-\,\dfrac{1}{cos^2x}\,\right)\,=\,0\phantom{X}$

resposta: a) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\,\frac{2\pi}{3}\,+\,2k\pi\rbrace\,$
b) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\frac{3\pi}{4}\,+\,2k\pi\, \rbrace\,$
c) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\frac{\pi}{6}\,+\,2k\pi \rbrace\,$
d) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\frac{\pi}{3}\,+\,2k\pi \rbrace\,$
e) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\frac{\pi}{3}\,+\,2k\pi\,ou\,x\,=\,\frac{\pi}{2}\,+\,k\pi\,\rbrace\,$
f) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\frac{\pi}{3}\,+\,2k\pi \rbrace\,$
g) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,2k\pi \rbrace\,$
h) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,2k\pi\,ou\,x\,=\,\pm\frac{\pi}{3}\,+\,2k\pi \rbrace\,$
i) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\frac{\pi}{3}\,+\,2k\pi \rbrace\,$
j) $\,S\,=\,\lbrace\,x\,\in\,{\rm\,I\!R}\;|\;\,x\,=\,\pm\frac{\pi}{3}\,+\,2k\pi \; ou \; x\,=\,\pm\frac{2\pi}{3}\,+\,2k\pi\rbrace\,$

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Veja exercÍcio sobre:
trigonometria
equações trigonométricas